Best way to unwrap half a sphere or a helmet?
Final:



Overview:

In this particular case I would go with Follow Active Quad unwrapping. You can 'cut off' the top of the helmet (there is another mesh there) so it's the easiest way I can think of.

Steps:



First of all Mark Seams around the top of the helmet and one through the back of the mesh.


Select all faces and Unwrap them.
Select one face, preferably near the Seam, it will keep texture more seamless.
Align this face in UV Image Editor by selecting edges and W > Align Auto.
Select all faces on your mesh (keep aligned face as active face).
Unwrap it by Follow Active Quads.
Hit Ctrl+P to Pack UV Islands.
Manually correct the top of helmet UV map.